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Practice Questions
Solve each rational equation
\(\textbf{1)}\) \( \displaystyle \frac{1}{x+2}+ \frac{x+1}{5}= 1\)
\(\textbf{2)}\) \( \displaystyle \frac{x-1}{6}- \frac{5}{x+2}= \frac{x-6}{3}\)
\(\textbf{3)}\) \( \displaystyle \frac{4}{x+1}+ \frac{2}{x+2}= 5\)
\(\textbf{4)}\) \( \displaystyle \frac{6}{x+1}+ \frac{4}{x-3}= 3\)
\(\textbf{5)}\) \( \displaystyle \frac{4}{x+1}- \frac{8}{x+3}= 0\)
\(\textbf{6)}\) \( \displaystyle \frac{x}{x+1}- \frac{x-1}{3}= \frac{1}{x+1}\)
\(\textbf{7)}\) \( \displaystyle \frac{x}{x-3}- \frac{x+1}{12}= 2\)
\(\textbf{8)}\) \( \displaystyle \frac{2}{x+2}- \frac{3}{x-1}= 4\)
Challenge Problems
\(\textbf{9)}\) Solve for x. \(\,\, \displaystyle 4= \frac{x^2-9}{3-x} \)
\(\textbf{10)}\) \( \displaystyle \frac{5}{x-4}+ \frac{1}{x+3}= 2\)
See Related Pages\(\)
\(\bullet\text{ Rational Expressions- Multiplying and Dividing}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x^2+3x-4}{(x+4)(x+5)}\cdot \displaystyle\frac{x+5}{x-1}…\)
\(\bullet\text{ Rational Expressions- Adding and Subtracting}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{x-5}{x+3}+\frac{x+2}{x^2+5x+6}…\)
In Summary
A rational equation is an equation that involves one or more rational expressions. A rational expression is an expression that involves the division of one polynomial by another. When solving a rational equation, we need to follow a set of rules and procedures to isolate the rational expression and solve for the unknown variable. Rational equations are typically taught in an algebra class. In this class, students learn how to manipulate algebraic expressions and equations, and how to solve equations involving rational expressions is an important part of this topic, and it is often used to solve real-world problems involving ratios and proportions.
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